Biological
network alignment has the potential to be as useful as sequence alignment has
in relation to learning about biology, evolution, and disease. Although
about two dozen network alignment algorithms have been proposed, none as yet
have proven to fulfill this potential, due to many shortcomings.
Some of these shortcomings include: lack of knowledge about
how to best use network topology to recover biological information (EC? S3?
Graphlets? Spectral?); how to balance biological information such as sequence
against topological information; confusion in the literature between an
alignment algorithm and the objective function used
to guide the alignment, as well as confusion between how to produce the
alignment vs. how to measure its quality post-alignment; lack of a
good multiple network alignment algorithm; lack of an effective
method to eliminate the 1-to-1 nature of global network alignment,
since 1-to-1 mappings are not faithful to the evolutionary relationship between
biological entities such as genes and proteins; and finally, due to the
NP-complete nature of the problem, a lack of knowledge
about how far we are from producing the best alignments possible.

In this talk, I will introduce a novel method that already solves
some of these problems and for which there is a clear path towards
solving all of the others listed above, and more. We clearly
delineate the measure(s) M that measure the
quality of an alignment, from the algorithm S that
searches the space of all alignments looking for good ones according
to M. This allows us to directly compare many measures M.
We also demonstrate that our new algorithm S outperforms all
existing algorithms by all the various measures M that we've
tried. Furthermore, we demonstrate that on synthetic networks where the
answer is known, our algorithm recovers the best possible value
of all objective functions we've tried --- and thus demonstrate that none of
these objective functions are capable of actually recovering the best solution
because none of them have sufficiently high correlation with the only measure
we're actually interested in -- biological correctness.

The path towards having
network alignment add significantly to biological knowledge is still not clear,
but we argue that our algorithm is the first to show significant promise.